X-ray CT imaging systems are widely applied in various fields including medical service, safety inspection, and industrial lossless detection. A serial of projection data are captured through ray sources and detectors along certain tracks, and then restored through an image reconstruction algorithm to obtain a spatial distribution of linear attenuation coefficients of some section of an object. Image reconstruction refers to a process of restoring original attenuation coefficients from line integral data of linear attenuation coefficients, which is an inversion problem. Currently, a conventional Filter Back Projection (FBP) algorithm is mostly used in real applications, and it is an analytic algorithm based on processing of continuous signals. Iterative reconstruction technology also attains rapid development with a speed-up in computer processing. Compared with the analytic algorithm, the iterative algorithm can be used in more diversified conditions, and achieve a satisfactory reconstruction result even with various non-standard scanning tacks, low dose, incomplete projection data, or limited angles.
Recently, one of hotspots in CT imaging research is an CT image reconstruction method based on compress sensing. In accordance with the compress sensing theory, if some conditions are met, and a measured signal presents sparseness under some transform, the possibility that an original signal can be reconstructed accurately with only a few measurements is very high. Assume that the original signal has n components, and there are m measurement data, how can the original signal x* be reconstructed? Prior information and a “good” measurement matrix are essential. Here, the prior information refers to sparseness of a transform Ψ. It is required that the number of non-zero components of the signal after the sparse transform is not larger than the number of times by which incoherent measurement is performed on the signal:
                                                                    Ψ              ⁢                                                          ⁢                              x                *                                                          0                <        m                            (        1        )            
The measurement matrix should be as random as possible. A Gaussian random matrix, for example, may be a measurement matrix which satisfies the randomness requirement.
The original signal may be obtained by solving a constrained zero-norm minimization problem. The sparsest solution in zero-norm can be obtained from a set of all feasible solutions satisfying data measurement conditions:
                              x          *                =                  arg          ⁢                                          ⁢          min          ⁢                      {                                                                                                                          Ψ                      ⁢                                                                                          ⁢                                              x                        *                                                                                                  0                                :                Ax                            =              b                        }                                              (        2        )            
However, the zero-norm optimization problem is difficult to solve, and thus 1-norm is generally used to approximate the above problem:
                              x          *                =                  arg          ⁢                                          ⁢          min          ⁢                      {                                                                                                                          Ψ                      ⁢                                                                                          ⁢                                              x                        *                                                                                                  1                                :                Ax                            =              b                        }                                              (        3        )            
Total Variation (TV) is often used as sparse transform in CT reconstruction, and refers to integration of gradient modulus of a signal. The fundamental TV-constrained reconstruction method is to obtaining a solution which minimizes the total variation from a set of all feasible solutions meeting fidelity of measurement data of CT projection data:
                              min          ⁢                                                                  ∇                x                                                    1                          ⁢                                  ⁢                              s            .            t            .                                                  ⁢            Ax                    =          b                                    (        4        )            
The reconstruction method based on TV minimization constraint achieves excellent effects in sparse sampling, low dose and inner reconstruction problems. Except the sparseness as prior information, information of a prior image may also be used to enhance quality of the reconstructed image. For example, a reconstruction method based on prior image constrained compress sensing (PICCS) utilizes similarity between prior and target images for reconstruction. When a differential image xp−x between the prior image xp and the target image x has a sparseness, or is rendered sparse through some transform, the prior image can be used to enhance reconstruction effects. PICCS has been successfully applied in cardiac dynamic imaging, perfusion imaging, dual-energy CT, and C-arm CT. PICCS requires a high similarity between the prior and target image, especially numerical approximation to each other. As such, the differential image can has better sparseness. PICCS is not applicable any more when the prior and target images have a large numerical difference, such as MeV-keV dual-energy CT.